Spectral Backtests of Forecast Distributions with Application to Risk Management

41 Pages Posted: 6 Jun 2018 Last revised: 29 Apr 2020

See all articles by Michael B. Gordy

Michael B. Gordy

Board of Governors of the Federal Reserve System

Alexander McNeil

ETH Zürich - Department of Mathematics

Date Written: March, 2018

Abstract

We study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modeled probability level. The choice of the kernel function makes explicit the user's priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and propose novel variants as well. In an empirical application, we backtest forecast distributions for the overnight P&L of ten bank trading portfolios. For some portfolios, test results depend materially on the choice of kernel.

JEL Classification: C52, G21, G28, G32

Suggested Citation

Gordy, Michael B. and McNeil, Alexander, Spectral Backtests of Forecast Distributions with Application to Risk Management (March, 2018). Available at SSRN: https://ssrn.com/abstract=3187672 or http://dx.doi.org/10.17016/FEDS.2018.021

Michael B. Gordy (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States
202-452-3705 (Phone)

HOME PAGE: http://https://www.federalreserve.gov/econres/michael-b-gordy.htm

Alexander McNeil

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland
+41 1 632 61 62 (Phone)
+41 1 632 10 85 (Fax)

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